Manufacturers usually go for P-P poweramps principally for the efficiency (you get more W out of 2 tubes PP than in SE), other factors include hum reduction and slightly different harmonic content.
A high gain amp will typically have more preamp stages, therefore more SE character as preamps are SE Class A cathode biased.
You could place the PI earlier in the preamp thus reducing the number of SE stages but this has cost implications as you then need to double up the number of tone controls & components, plus the more stages you have & the more components, the more likelyhood of imbalance (though this could feasibly be addressed later in the circuit).
This has been done...at least twice.
Then what do you do about reverb, or NFB if you want these features?
Would there be any point in doing this in a SE design, if you're just going to mix the 2 sides again at another SE preamp stage before going to the poweramp? Most SE amps are designed the way they are to be cheap.
Why would you necessarily want to run the poweramp clean? If all the distortion is coming from the preamp a lot of folks would find this harsh & buzzy.